A quantum computer is a computational system which uses quantum-mechanical phenomena, such as superposition and entanglement, to process data. Unlike digital computers in which data is encoded into binary digits (bits) in one of two definite states (“0” or “1”), the quantum computation requires data to be encoded into qubits (quantum bits), where a single qubit can represent a “1”, a “0”, or any quantum superposition of the two qubit states. In general, a quantum computer with N qubits can be in an arbitrary superposition of up to 2N different states simultaneously, i.e., a pair of qubits can be in any quantum superposition of four states, and three qubits in any superposition of eight states.
Large-scale quantum computers are able to solve certain problems much more quickly than digital computers. In the operation of a quantum computer, the computations are initialized by setting the qubits in a controlled initial state. By manipulating those qubits, predetermined sequences of quantum logic gates are realized that represent the problem to be solved, called a quantum algorithm. Quantum algorithms, such as Shor's algorithm, Simon's algorithm, etc., run faster than any possible probabilistic classical algorithm. Quantum algorithms are often non-deterministic, as they provide the correct solution only with a certain known probability.
The computation is finalized with a measurement, which collapses the system of qubits into one of the 2N pure states, where each qubit is purely “0” or “1”.
An example of an implementation of qubits for a quantum computer could start with the use of particles with two spin states, such as “down” and “up”, typically written |↓ and |↑, or |0 and |1. But in fact, any system possessing an observable quantity A, which is conserved under time evolution such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit. Any such system can be mapped onto an effective spin—½ system.
In quantum computing, and specifically in the quantum circuit model of computation, a quantum gate (or a quantum logic gate) is a building block of quantum circuits. The quantum gates operate on a small number of qubits, and are represented by unitary matrices. The action of the quantum gate is found by multiplying the matrix representing the gate with the vector which represents the quantum state.
A gate which acts on k qubits is represented by a 2k×2k unitary matrix. The number of qubits in the input and output of the gate has to be equal. For example, the quantum gates operating on spaces of one or two qubits, can be described by 2×2 or 4×4 unitary matrices, respectively.
A quantum computer is composed of at least two quantum systems that serve critical functions: a reliable quantum memory for hosting and manipulating coherent quantum superpositions, and a quantum bus for the conveyance of quantum information between memories.
Quantum memories are typically formed out of matter such as individual atoms, spins localized at quantum dots or impurities in solids, or superconducting junctions (Ladd, T. D. et al. Quantum computers. Nature 464, 45 (2010)). On the other hand, the quantum bus typically involves propagating quantum degrees of freedom such as electromagnetic fields (photons) or lattice vibrations (phonons). A suitable and controllable interaction between the memory and the bus is necessary to efficiently execute a prescribed quantum algorithm.
A number of different types of quantum computers have been developed. For example, a trapped ion quantum computer is a type of quantum computer in which ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be processed and transferred through the collective quantized motion of the ions in the trap (interacting through the Coulomb force).
Lasers are usually applied to induce coupling between the qubit states (for single qubit operations), or coupling between the internal qubit states and the external motional states (for entanglement between qubits).
Trapped atomic ion crystals are considered the leading architecture for quantum information processing, with their unsurpassed level of qubit coherence and near perfect initialization and detection efficiency. Moreover, trapped ion qubits can be controllably entangled through their Coulomb-coupled motion by applying external fields that provide a qubit state-dependent force.
In the past two decades, trapped ion experiments have featured high quality qubits, and have demonstrated high quality quantum logic operations. Hyperfine qubits utilizing two ground states of an atom have been shown to routinely exhibit long coherence times of a few seconds, and more than an order of magnitude longer when operated in the “field-independent” regime where the energy splitting of the two qubit states is independent of the magnetic field fluctuations to a first order.
High fidelity qubit preparation with near-unity fidelity is routinely achieved by optical pumping, although the experimental characterization is typically limited by the qubit state detection process. This is commonly referred to as state preparation and measurement (SPAM) errors. High fidelity qubit state detection with errors in the 10−4 range are available in the optical qubit with an average detection time of 150 μs, while a direct detection of hyperfine qubits can be performed with 10−3 errors range with an average detection time of 50 μs. Single qubit gates on hyperfine qubits driven by microwave sources show the lowest level of error, in the 10−5 to 10−6 range.
The best performance of two-qubit gate demonstrated to date features errors in the 7×10−3 range.
The current challenge in any quantum computer architecture is the scaling of the system to very large sizes due to possible errors which are typically caused by speed limitations and decoherence of the quantum bus or its interaction with the memory. The most advanced quantum bit (qubit) networks have been established only in very small systems, such as individual atomic ions bussed by the local Coulomb interaction, or superconducting Josephson junctions coupled capacitively, or through microwave striplines.
Scaling to large number of ions N within a single crystal is complicated by the many collective modes of motion, which can cause gate errors from the mode crosstalk. Such errors can be mitigated by coupling to a single motional mode, at a cost of significantly slowing the gate operation. The gate time τg must generally be much longer than the inverse of the frequency splitting of the motional modes, which for axial motion in a linear chain implies τg>>1/ωz>N0.86/ωx, where ωz and ωx are the center-of-mass axial and transverse mode frequencies. For gates using transverse motion in a linear chain, it is found that τg>>ωx/ωz2>N1.72/ωx. In either case, the slowdown with qubit number N can severely limit the practical size of trapped ion qubit crystals.
There have been successful demonstrations of controlled entanglement of several-ion quantum registers in the past decade involving the use of qubit state-dependent forces supplied by laser beams. These experiments exploit the collective motion of a small number of trapped ion qubits, but, as the size of the ion chain grows, such operations are more susceptible to external noise, decoherence, or speed limitations.
A promising approach to the scaling of the trapped ion qubits is the use of a quantum charge-coupled device (QCCD), where physical shuttling of ions between trapping zones in a multiplexed trap is used to transfer qubits between short chains of ions. This approach was first suggested in D. Kielpinski, et al., Nature (London) 417, 709 (2002), but even in that architecture it is desirable to increase the number of qubits per zone. The QCCD approach is expected to enable a quantum information processing platform where basic quantum error correction and quantum algorithms can be realized.
The QCCD approach, however, careful control of the time-varying trapping potential to manipulate the position of the atomic ion and involves advanced ion trap structures, perhaps with many times more discrete electrodes than trapped ion qubits, and therefore requires the use of micrometer-scale surface traps. Novel fabrication techniques would be needed to support the implementation of the QCCD approach. Furthermore, this approach cannot easily be extended over large distances for quantum communications applications.
Further scaling in the near future will likely be limited by the complexity of the trap design, diffraction of optical beams (Kim, J. & Kim, C., Integrated optical approach to trapped ion quantum computation. Quant. Inf. Comput. 9, 181-202 (2009), and the hardware controllers to operate the system.
Among numerous attempts to overcome the challenges facing quantum computer scaling, the scalable quantum computer architecture framework has been developed which is presented in U.S. Pat. No. 7,875,876 issued to Wandzura, et al. This system includes components necessary for computer computations, such as local computer computations, distributed quantum computation, classical control electronics, classical control software, and error-correction. Specifically, Wandzura, et al., employs at least a pair of classical to quantum interface devices, each connected to a distinct quantum processing unit (QPU). An Einstein-Podolski-Rosen (EPR) pair generator is included for generating an entangled EPR pair that is sent to the quantum processing units (QPUs). Each QPU is quantumly connected with the EPR pair generator (EPRPG) and is configured to receive a mobile qubit from the ERRPG and perform a sequence of operations such that the mobile qubit interacts with a source qubit where a teleportation algorithm is initiated, leaving a second mobile qubit in the original quantum state of the source qubit.
The Wandzura design does not suggest truly modular quantum computer architecture which would be built with a plurality of modular quantum memory registers dynamically configurable and reconfigurable into multi-dimensional computational hypercells for fault-tolerant operation capable of mapping to 3-dimentional cluster states of ion qubits in accordance with the predetermined quantum algorithms. Moreover, Wandzura's system is silent on any mechanism for the crosstalk suppression, and it is not believed to be capable of scalability to large numbers of qubits.
Thus, a quantum computer architecture scalable to a large number of ions and free of the shortcomings of the existing approaches is still a long-lasting challenge in the field of quantum computers.